Radiometry and photometry in astronomy

1997-09-10 First version
1998-03-29 Added a paragraph about photography + some minor corrections
1998-05-06 Added Jeff Medkeff's paragraph about visual observing and the physiology of the eye. Also added several new references.
1998-06-10 Some corrections to the relation between candela and lumen. Also added a paragraph about Lambert's law.
2000-03-11 Added a table of horizontal illumination from sunlight during clear weather at different solar altitudes above the horizon.
2000-11-12 Added a link to another radiometry/photometry FAQ + removed some dead links.
2000-11-15 Added a list of the brightness of the radio sky. Also added something about conversion from radiometric from photometric units.
2001-01-18 Corrected a confusion of luminance and illuminance at a few places. Also added a table of the correspondence between radiometric and photometric units.
2001-02-02 Added Tom Polakis paragraph about big telescopes and light pollution. Also rearranged the paragrahs at the end.
2003-04-24 Corrected a typo: 1 stilb isn't 1 lumen/cm/ster but 1 lumen/cm2/ster
2004-02-18 Added a reference to the Explanatory Supplement
2004-06-16 Updated or removed outdated links
2006-12-08 Adjusted the luminance of a candle down from 6E+5 to 2E+4 cd/m2 (thanks to Jan Hollan for measuring this)
2009-03-18 Corrected a small error regarding units for photon flux
2010-04-13 Corrected an error regarding converting between watts and lumens
2017-03-05 Updated numerous obsolete links and removed those for which no update could be found. Corrected a few typos as well.

Scotopic vision ("Night vision"): only rods active. To be used below 3 cd/m2

V(lambda) = 0.992 * exp( -321.9*(lambda-0.503)^2 )

The conversion is performed using the integral:

infinity
/
|
Xp = K * | Xr(lambda) * V(lambda) * dlambda
|
/
zero

where Xp is the photometric quantity, Xr(lamnda) the corresponding
radiometric quantity and V(lambda) the sensitivity function of the
eye (photopic or scotopic, depending in the light level). K should
be chosen so that one watt corresponds to 683 lumens at a frequency
of 540 THz (= a wavelength of 555 nanometers) for photopic vision,
and 1700 lumens at 507 nanometers for scotopic vision. Since
V(lambda) equals unity at these peak wavelengths, K simply becomes
683 for photopic vision and 1700 for scotopic vision.

In principle, the integration should be performed from zero to infinity. In
practice, it's sufficient to integrate from 360 to 830 nanometers.

Naturally, photometric quantities are meaningful only to sources of
visible light. It's meaningless to try to figure out how many lumens
e.g. a radio source emits, because it doesn't emit in the visual
wavelength range.

Also, such effects as the Purkinje Effect can change the apparent
brightness of certain colored stars to a degree much greater than the
star's B-V alone could account. (See "What is the Purkinje Effect" below.)

Long answer: The simple-minded claim is that under conditions of bad
light pollution, beyond some certain aperture, you gain very little
or nothing over a smaller telescope. The claim also is that this
crossover aperture becomes smaller under progressively worse
conditions of light pollution.

The physics is pretty simple: "aperture always wins". It is a simple
matter of signal-to-noise: in any scene a telescope does not
magically brighten the sky background while not brightening the
celestial target at the same time. Yet the claim being made by most
folks is that the background is indeed enhanced.

Take this notion to an extreme of really bad light pollution:
daytime! If the expections of this urban legend hold, then
"theoretically" the naked eye should show things in the sky better
than any telescope. But you can see no stars with the naked eye in
daylight (let's talk noontime here, not 10 minutes before sunset),
whereas you can see stars in even small a telescope without much
difficulty. (Try it! First a bright star like Vega. Figure out how
to get to it with your telescope, and go look at it some clear day at
11 in the morning. Is Vega easier to see in a 6x30mm finder or a
16-inch? Now go for Altair, then Deneb...and how much fainter?)

If you wish to learn a lot more about this subject -- which will help
you become a better observer -- go to Mel Bartels' Web site
http://www.efn.org/~mbartels/aa/visual.html and read the
stuff by him and by Nils Olof Carlin about visual detection
thresholds. Apply the equations there to dark, light-polluted, and
daytime sky brightness values to see what happens, and to prove to
yourself that this light-pollution/aperture claim is pure baloney.